Can I sell low cost airlines and the normal airlines together on my portal?

Yes, most flight booking APIs let you sell low cost airlines and full service airlines side by side, so your customer sees both in the same list of results and does not have to know which is which before they choose.

Behind the scenes the two behave differently, and it helps to know that before you start selling. Low cost airline fares are usually sold on the spot, which means the seat is paid for and confirmed in one step, and there is often no way to hold it while your customer thinks about it. They are also more likely to be non refundable, and things like a checked bag, a meal or a chosen seat are sold as extras rather than being part of the fare. Full service airline fares more often allow a hold, a proper refund calculation and a date change, and they usually include a bag already.

What you actually get depends on your supplier and on the part of the world you sell in. No supplier carries every low cost airline, so there will be carriers your customers know locally that simply do not appear in your results, and some suppliers price low cost content differently or keep it on a separate plan. On your side you can normally set a different markup for the two types, which is worth doing because the margins are not the same.

Before you build your selling around it, write down the airlines your customers ask for most and ask your supplier to confirm which of those they can really book and issue for you.